Lots of returned mail (spam) - problem?

I just checked a particular e-mail account for the first time in a couple days, and I found that I’ve gotten about 34 e-mails with variations of “Returned Mail” messages. For the account receiving these, I have sent only a handful of e-mails in the last few weeks, and these are clearly not bounce messages for those particular e-mails. (FWIW, this account does get conventional spam - perhaps 10-25 spam messages per day).

The addressees on the returned mail are, from casual inspection of a few of them, people I don’t know (not in my address book), mostly with .ua e-mail addresses (Ukraine, perhaps)?

My question is - is this a new form of spam that I can safely ignore (i.e. they’re trying to get me to open the attachment of the returned mail), or does this possibly indicate that my PC has some kind of virus, or that someone is just sticking my address on the end of spams, or that my e-mail server (a hosted account) has been attacked, or something else?

I don’t want to spend hours chasing down a phantom problem, but don’t want to ignore a real issue either.

That’s most likely. I get the occasional bounce like that, and it sounds like some spammer just decided to use yours a lot for whatever reason, or sent out an even bigger flood of them than usual.

Seconded.

There’s a bunch of spam and hacking attempts originating from Ukrainian and Bulgarian IPs on one of my servers lately.
Spamcop it and delete.